The Toffees have already completed moves to make Merlin Rohl and Tyrique George's loans into permanent transfers with Hayden Hackney also landing in from Middlesbrough.
A £7M deal for Arsenal's Christian Norgaard could be the next completed move, as the Gunners want to offload the Norwegian to free up space for Bruno Guimarães, and Moyes wants more experience in his engine room after Idrissa Gana Gueye's exit.
Those new arrivals will be balanced against exits and Tim Irogegbunam could be moved on, with Teamtalk.com indicating promoted trio Hull City, Ipswich Town and Coventry City are all interested in making an offer for the 23-year-old.
The former Aston Villa midfielder is now into the final year of his contract on Merseyside, so Everton are not interested in loan offers, to avoid losing him for free in 2027.
That situation could force Moyes to lower his asking price which is currently set a around £20M for a player with just 59 top-flight appearances to his name at Villa and Everton.